electron hạt hay sóng





!"#!$%
 &'(!)!*!!+
!,#!)&'-.*
!)/#0
1
2
3 '
2
45
!6 789::;
9
MU
̣
C LU
̣
C
<
=
<
=
9
>?<4
1@AB%C-D@D%E.F
G@D%E.%H IJ3!6EE.KL%M*NE@OP9
5+%!QE%M*D@D%E.9;
IKE.R!+!,E%M*D@D%E.44
<SF:

TU<VF9




 GVHD:TSKH. Lê Văn Hoa
̀
ng
4
LỜI NÓI ĐẦU
 '*'CWKIJ3!6EE.KL%M*X!*!Y%%Z  ![\%6% !X!*!Y%
%1]+\E. ^
2
%
2
C_
=
E@'
2
%` %"!a ]AW%3!6EE.KLCABE]N%A
=
3!*
2
EE.K
b

%&
b
*%1!
=

%@A1
=
 EA
b
^*
c
^A*% A1
d
KX!*
2
#3!*
2
!K
d
&!1E!
2
 K1
2
KCK#Z
!A
c
 !K
b
&]K
2
E]A1
2
%^_
d
&C

d
Ee
2
!%!_
2
E%&
b
*%*
2
%^Z
2
KEA1
=
 CK#Z^*
c
 K&
2
3%!&
2
 E*
!A
c
 %1I1
b
^
b
A
2
 f&
=

 %!&
2
 C*
d
X!*!
=
%C*
d
%Z  !
=
!K
=
^*
=
K\^
=
%]K
=
E@*
d
IA
=
.*^1
d
K%&
b
*#*
2
'Ee
2

!@A1
=
 EA
b

KEA
d
E!
2
 K1
2
KCe
c
#ZI* CK#Z\% A1
d
K%&
c
 ^KEA
d
 *
=
%!K*
d
'
I*  *
=
%!KX!*
2
%Ce
d

%*
2
%!!*
d
!gA
b
%&
b
*E!
2
 K1
2
KCK#ZG@D%E.@*
d
#Z
=
E^Z
2
K
EA1
=
 h&DE!&Z
=
%C1
2
K%!&
2
 E*. %1!
=
%%Z

b
^K
b

2
@*
d
#Z
=
E!*
=
E\!A X!K
%1!
=
%@A1
=
 EA
b
.*^1
d
K@K
=
&
2
%
2
@*
d
#%!&
2

 E* *
=
%!KX!Z i5*
b
%!_
2
E%&
b
*

2
@*
d
 e
d
i*%
2
!K
b
&^_
d
'^&
b
C
d
]*
b
%!_
2
E%&

b
*D@D%E.%!A*i*
d
^_&@*
d
.*! K1
2
K
KA
c
*CK#ZC*
d
Ce
c
#Zi
5*
d
KEK
b
&@&_
=
.*^1
d
KCe
d
IA
=
^*##X!*
2
#3!*

2
\Ee
d
#E
d
K!
=
%!
b
KC*
d
%&
c
 
!
d
#E.*
b
@1
d
K%!!A
c
 %_&!
b
K^
2

1
2
K@A1

=
 XK
2
E!A
2
%%
d
!*
=
%!
2
\]*
d
KEK
b
&@&_
=
X!Z E.*
2
!X!
b
K!A
c
 
I*KI
2
E !_
=
^A1
=

%IA
=
!_
=
gD
2
EC*
d
 
2
3'
2
%&
b
*!_
d
'C*
d
%*
2
%]*
=
j
!_E!*
d
!%*
2
#1j
!
2

#EK
b
&@&_
=
j





 GVHD:TSKH. Lê Văn Hoa
̀
ng
F
I. Sơ lược về electron:
Cấu trúc: 
Loại: 
Nhóm: 
Lớp: 
Tương tác:  !
Phản hạt: "#
Lý thuyết: $%%&'()(*+',-./#0&'(12,
345.
Thực nghiệm: /./.6#&'(71,
Ký hiệu: 
8
9
8
Khối lượng: 7.':7)(;'+&2+,<':
=)'

>
 +.2(+177:72)&;),?':
82

 :.+':77(7':&'),@AB
;
Điện tích: ='C='.D:;'1D2(1&2:,<':
='7
E
Spin: F
K[Ek@#lE!,E%"Xm%!E!AW%!n!1 &'Ek\#* ^K[Em%!_#
 AoKE*%!.p X!Z %"%Q&E.0%!n!1^K[EkC"@#lE^K[Em%!
^KL#6%^K[Ek^-&E!*# K*EA1 E6% Q3fq\EA1 E6%^K[ErCEA1 
E6%'s&Kt !AX!tK@AB  !uC^K[Em%! &'Et%M*"\##DEEr
v!*'I3Kw%M*#lE^K[Ek%" K6E.)X!Z ^xK!K#lE^K[EkC*%!,#CWK
3!+!,E%M*"@3IKE.\%+!*K^-&])!M'lE%y3^K[EkC3IKE.^AB%
E,.*]zKEK* *##*%" @AB Cr*^M
K+E!&'sEC-#lE@AB ^K[Em%!CZ!{!E.  &'Ek^AB%^A*.*
^L K+KE!m%!Em!%!QE!"*!Y%%+ &'EkK+E!&'sE'f!E.KsE!Y%EJ
!K AoK!K%!*.f*#K ^A*.*C#P|4|6KE}D@D%E.~^AB%
!CNE@O AoKK@DD .D•!IEDED'^y%!@,K^K[Em%!'C
#P|€F#P|;€\••!#IC%6%^• IJ AoK!^‚g6%^)!
D@D%E.v^K[Ekw@#lE@,K!,EK[Ek^AB%gD#@E!s![!Y!,E@D3E^ƒ&
EKK[Ek%"%6%Em!%!QE%1!Y%@AB Ek%M*%+!,ECI" „C{CN'"%"
E!LC*%!,#CWK%6%!,EX!6%C%` %"E!L!K(&g,!AI" 6!I6 …K




 GVHD:TSKH. Lê Văn Hoa

̀
ng
7
^K[EkE•E,Kz#lEE., E!6K@AB Ek\#ZE+Em! q&!K%M*"]p #lE
E!Z ItCNE@O^"!A @AB lKE,K!*'!AW %M*I3K{^K[Ek@
!,E†D.#KX!Z %"9^K[Ek%H z#lEE., E!6K@AB Ek„Em!
%!QE'%!m!@ &'@O@,KE.r*&@K
. !K-&!K[EAB CNE@O\Cmf‡!A^K[\Er\fq!K[E\^K[Ek
^" C*KE.ˆ.QEh&*E.Y lE^K[Ek%"E!LE,.*#lEErE.Ao X!K"
%!&'L^l !K^K[Ek^AB% K*Et%\"%"E!LEn*!y%E!& @AB fAWK
f, 3!EK[Ek%H CWK!,E!_ &'Ekv •#3.ECD&E.wE,
E!! &'Ek&'!K\^K[Ek%!u%!Ks#:\:‰ŠX!tK@AB %M* &'Ek
J%&@#] Ka*^K[EkC3.E^‚ Ka%!"]) KWK!,E.  &'Ek
JE.*^xK!y%E.*^xK^K[Ek Ka*!*K!*'!K-& &'Ek@%1Iz%!m!
%M*%6%@KXsE!"*!Y%
K[Ek^AB%E,.*E. C‡x5K 5* \C"%"E!L])EK&!M'E.
h&6E.{!Ex !B3!,E!_E. %6%I*K[EkE!Ao ^AB%E,.*Er%6%
]$%g,*‹XK z%!_E.oKIJXK[%M*#lE@…^DC%6%]$%g,C`E.‡^KC
X!mh&'L%M*.6K^QE6%^• C)^AB%Xm%!E!m%!]zK%6%I" ^K[ErIŒE,
.*^K[EkEr#lE!,E!_ &'EkE. h&6E.{!3!_.‚!,E•Ž6%f‡ %‡
E. 3!ˆ E!m !K[#%"E!L KaCh&*I6E%6%^KEk.K @•\E. X!K^"
Xm!E!KC%"E!L3!6E!K[^K[Ek3@*I#*X!Kh&*I6EIJE+ @AB 
%M*"K[Ek3@*I#*%"!K-&$ f‡ !A!\t EK*%*EE\Xm!!KLCK
^K[Ek\@K[&3!633!" g,\@*ID.C#6' K*Et%!,E
.^_'@!a ^K-&I1@AB%#% AoK]KsEC-D@D%E.*IŒE{#
!KL&h&6E.{!% AoKE{#!KL&C-D@D%E.RErIJX!6#3!6.*D@D%E.^s
]+%!QE%M*D@D%E.@ {
  
 '*'\%6%t 3!" ^K[^AB%fH .l .‚K%!%6%h&+ %6
^ƒ'#&I•%z K^Ao 3!t &• t%%M*t 3!" ^K[^ƒ&EK@f





 GVHD:TSKH. Lê Văn Hoa
̀
ng
‰
‘K@@K*#.XDI%!sE,#P|€:’ E!J%!K[%!_X!Z %*]p #6'
!0EX!m@# K+#63I&QEE. t ^s#$%.QEE!Q3E. #lEt E!M'EK!C
!NE!Q'.p %6%%!QEX!mz63I&QEE!Q3IŒfq^K[lEE. !a t 
^ƒ&EK#.XDIE!m !K[#%"!*K^K[%J%XK#@,Kz^ƒ&t C!Xm
I*&X!K^‚ K+#63I&QEX!mE. t !K^yE#lE!K[&^K[E!s%* Ka*!*K
^K[%J%\X!mE. t 3!6EI6 C#&6!I6 3!6Eg,3!‡E!&l%C@,K
X!m^AB%fH 
N'f^_&#%"6!I6 3!6Eg,E. t i.XDI^‚E!KsEXs#lE
t E. ^"%"^yE#lE%6K%! %!" !n*E!Q'EK*3!6E.*Er%*EZEvtK
CWK%J%_#%M* &•^K[w^‚@#h&*'%6!h&,E%M*%! %!" !A 
X!K^yE#lE*#%!_# ƒt E!{%! %!"  r h&*'\%!$ En%6%EK*
@0%E.AW%^N3C%6!h&,E@#%! %!" h&*'*'^‚])@[%!!AW N'
EK*^"3!+K@!a !,E#* ^K[C{%!0 %!)&E6%f‡ %M*ErE.Ao !K-&
E!m !K[#X!6%^‚%!$ En%6%EK*'#* ^K[_#\Cf%!0 3!6E.*Er
%*EZE%"E@EK*%*EZE
tKh&*E_#%M*%6%!CNE@mC-]+%!QE%M*EK*%*EZE^‚X“fK
E. !K-&##%!A*^AB% K+Kh&'sE‚KEWK!19:#I*&vP|;€w\
•!#I^‚X!6#3!6^AB%]m#NE'5p #lE@Y*EE!m !K[#\Z ^‚
%!$ #K!.p EK*%*EZE •#!a !,ECZ%H !n]“Em%!^K[_##Z 
YK@%6%}%.3&I%@D~ '*'E* YK%!0 E* YK@%6%D@D%E.’ %!$ 
#K!^AB%.p D@D%E.@^• !QE]QEXLX!KfH E. t E!&l%@,K {
!#I@,K^-g&QE#lE@&N^KL#E6],Ch&*E.Y \#I*&'

%!$ En"@%!m!g6%\"K.p %6%!,EZ E{#.*@#lEE!!3!ƒ%M*#YK
^tKEAB CNE%!QE*&^"@,KXsE@&NE!#!,EQ'!”!1!,E!”!QEE!oK
]Q' Ko@ &'Ek!Kf.!  @ƒvI*&' AoKE*]KsE%!m!g6%@
P|4‰P7w’ ^‚^^K[Em%!.K D8#%M*D@D%E.\%H CWK!*K@&N^KL#EK
E{!C%!m!g6%^‚@#}IJ3!6E!K[D@%E.~\^‚@#Z xKf*!X!•3
1K•&*K[#E•E,KEr!K-&E!sXuE.AW%%!.p  &'Ek@3!ƒEkCNE




 GVHD:TSKH. Lê Văn Hoa
̀
ng
€
%!QE%&tK%H X!Z E!L3!_%!K*^AB%^s*'^‚%!Q#f$E!m !K[#%M*
!#I^‚^yE-#" %!IJ3!6EE.KL%M*X–E!&NE^K[EkI*&'#EK&
]KL&@f*^l XmCt ^—!{!%M*#6'E!&!{!vEKCKw!˜ ]*@_&I*&
3!“3^E.J%EKs3^K[Em%!%M*D@D%E.^AB%E!J%!K[\CCK]*#I*&\
D@D%E.^AB%%!m!E!$%%Z !N@#lE!,E%M*EJ!K
  !"" # 
‡  %‡ •# #lE ]{! E!M' EK! %!$* X!m !'f. z63I&QEE!Q3
v!{! Pw!H#^K[Ek3!6Eg,Erf_'^tEv%*EZEw^Kg&'h&*X!D%M**ZE
Y%^Ao ^K%M* ]{! %!$* X!m\ %6% D@D%E. C* %!,# CWK %6%  &' Ek
X!m\ Xm%! E!m%! %6% &'Ek'C@#%!0 3!6Eg,X!Ks%!^Ao ^K
%M*%!H#D@D%E. E.Z E!Q'@#lECsE#+!I6 lE%y3%&lf_'vX!Z
CŒE.!{!w^AB%]tE.mz!*K]%,!]{!C%!fˆ ^K[X!Z ^xK^K
h&*^LE,.*#lEErE.Ao ^-&%"%+# $  Er C&Z  "% CWK ]{! 5t E.m
%! 3!A1  ]* ^ƒ& %M* %!H# D@D%E.C&Z  "% CWK ^Ao  %+# $  Er
!K ^" @J% .DE™ E6% f‡  @ D@D%E. %" !AW  C&Z  "% CWK CN Et%
C ^"  C*K E.ˆ @J% !AW  E_# @# %! D@D%E.%!&'L^l E!Dh&š^,

E.ˆ
9
3
 G3

= =
vPPPw
&'.*]6Xm!h&š^,
3

G
=
vPP9w
!0O@@J%.DE™@&ZC&Z  "%CWKCNEt%\f^""X!Z 
E!J%!K[%Z C%!&'L^l %M*D@D%E.@%!&'L^l E.ˆ^-&CWKCN
Et%CX!Z ^xK*E!Q']6Xm!h&š^,%!u3!‡E!&l%%+#$ Er5Er
E.Ao % #,!E!{]6Xm!h&š^,% !n




 GVHD:TSKH. Lê Văn Hoa
̀
ng
|
L^^K[Em%!.K D8#%M*D@D%E.\E*fH ]{!"KE.ve
d
!
P9wC@ƒ@ABE^K-&%!u! K6E.)%+#$ Er5]p %6%!fH #lE]KsE.z
^LE!*'^xKfˆ ^K[%!,'E.  %6% %&l f_' …K @ƒ E!*' ^xK @,K ^

^Ao  Xm! %M* %!H# D@D%E. E.E!* ^]E. ]{!. E!J%Es
E!m !K[#\ AoKE*^K-&%!u!^L^Ao Xm!%M*%!H#D@D%E.@!a 
K6E.)f(^C^Y% K6E.)fˆ ^K[EA1 $ E. %&lf_'*!‚'Em!
E6^LE{#%Z E!$%g6%^)!^K[Em%!.K D8#
rvPP9wE*%"
G
3

=
vPP4w
NEt%'I&'Er^l   #D@D%E. E!&^AB% X!K%!&'L
^l h&*^K[E.Ao %"!K[&^K[E!s

vE!s*ZEw
9
9
9
9
H
H
A3
A 3

= ⇒ =
vPPFw
sE!B3vP9wCvP4wE*^AB%
9 9
9
H
A

 G 
=
vPP7w




 GVHD:TSKH. Lê Văn Hoa
̀
ng
e
d
!P9
;
. E!m !K[#
ŽK[E!s


^E.J%EKs3]p C@EXs
Ž56Xm!.%M*h&š^,^E.J%EKs3E.E!* ^
Ž+#$ Er5Em!Er K6E.)%Ao ^lh&*%&lf_'^Y%E.*#3D.D
Xs
Žƒ@ABEE!*'%6% K6E.)%M*5CCŒ^•E!)5›†vP8.w
•E!)'%"f, #lE^Ao E!˜ ^Kh&* t%EY*^lC{I&'ErvPP7w
9
H
A
G



=
P

vPP‰w
N' K6E.)D8#IŒ^AB%I&'Er^lft%%M*^•E!)
9
H
A


vPP€w
*&^_'@E!mf‡]p It &•3!6Eg,D@D%E.!,E^l z^K[E!s


›9:::fH ^L]•%!H#D@D%E.C#lEErE.Ao ^-&%"5›P\;P:
Ž
4
!A1 CNEt%]*^ƒ&%M*%!H#C&Z  "%CWK%+#$ ErC%!H#
D@D%E.CŒ#lECˆ E.ˆh&š^,%"]6Xm!|:##r!a  K6E.)E.\
E*g6%^)!^AB%^K[Em%!.K %M*D@D%E.E!DvPP7w
PP
4 9 4 9
99:::
P\€4P: 8
vP\;P: w v|:P: w

E >

− −
= =

$  !"" %#& 
1^•fAWK^_'%!E!Q'E!KsE])#!CNE@O AoK*œ\]D.E
f.D‹IK@KX*vP|‰;RP;74w^‚fH E. !a #P;P:RP;P4^L^
^K[Em%! &'EtD




 GVHD:TSKH. Lê Văn Hoa
̀
ng
P:
!K%6% KYEfƒ&!n^AB%3!&C]&• \f%Yg6ECWK#K[ CˆK
3!&#lEIt KYEfƒ&E.zEm%!^K[!y%_#!y%fA1 •“E#lE KYE
fƒ&%"^K[Em%!_#h

.1Kg&t ]&• h&*#lE@…!nE.]+
P

ƒ&EKX!K9]+XK#@,KX!Z ^AB%tKCWK &•\9]+
P
\
9

X!Z Em%!^K[*E!Q'!a !,Efƒ&.1Kg&t CWKEt%^l!*!fƒ. 
h&6E.{!.1K KYEfƒ&%!)&E6%f‡ %&*E.Y @J%!AW g&t C@J%%+ž
%

›]C!AW @!A1 E.{!%!&'L^l %M* KYEfƒ&
3

 I3 

− =
vP9Pw
E. ^"]^AB%g6%^)!]p ^)!@&NEEXD
‰I %
πη
=

η
@![It!WE%M*%!QE@n
*@]6Xm!%M* KYEfƒ&
!KEt%^l.1K%M* KYEfƒ&X!Z ^xK\E.Y @J%%_]p CWK@J%%+
Et%^l%M* KYEfƒ&@0%^"@
J

3
I
=
vP99w
*&^"tK9]+CWK &•^K[!A!{!CŒve
d
!P4w\ &•^K[
_'#lE^K[Em%!fAE.]+fq^K[
P
C#lE^K[Em%!_#fAE.]+fq
^K[
9
6%]+^K[Em%! _'.*#lE^K[E.Ao G!AW ErE.g&t fAWK
E. ]&• K[E.Ao 'E6%f‡ #lE@J%Em%!^K[@]QEX{#lE KYE

Em%!^K[.1KC]&• C+!!Az ^s%!&'L^l %M*" KYEEm%!
^K[_#E*^* g“E%"g&!AW ])^/'@E.!A1 E.{!%!&'L^l %M*
KYEfƒ&

3
K L  I3 

− − =
 vP94w
rCK[%^E!oK K*%!&'L^l %M*%6% KYEfƒ&X!KX!"*#zC
X!"*^" \E*%"E!LEm!^AB%^K[Em%!_#h%M* KYEfƒ&




 GVHD:TSKH. Lê Văn Hoa
̀
ng
PP
NEt%%&tK%M* KYEfƒ&\X!K@J%^K[%_]p CWKE.Y @J%C@J%
%+


K L 
3
I
−
=
vP9Fw
. E!m !K[#'\Et%^l%&tK^,E^s!ƒ&!A@ *'@N3E$%

%6% KYEfƒ&f)%!%!&'L^AB%#lEX!+ %6%!X!K%!&'L^l @!y%
g&t I6!%Z E!$%vP94wCvP9FwE*%"
P P
v w v w
J
 J 
J J 
6

K 3 3
L3 L 6 6
= + = +
vP97w
. ^"
†
›8C
†
@E!oK K*.1KC
.
›8C
.
@E!oK K*^K@
s&^K[Em%!%M* KYEfƒ&^AB%E @!oE!#C#lEIt^K-&
XK^"E!{CNEt%%&tK%M* KYEfƒ&@0%'@C
.
Ÿ\C%"#tKh&*![CWK
^K[Em%!#WKh

ŸE!D%Z E!$%



K L 
3
I
−
=




 GVHD:TSKH. Lê Văn Hoa
̀
ng
e
d
!P4
P9
&'.*


P P
v w v w
J
   
J  
6

K K 3 3

L3 L 6 6
− = − = −
vP9‰w
NEt%C
†
\C
.
\C
.
Ÿ^AB%g6%^)!]p %6%!^E!oK K*.1Kg&t C^K
@\CWKX!+ %6%! Ka*9]+fq^K[
s&CKsEh

›DCh

ŸRh

›ŸDCWKŸE!*'^xKE. E!{vP97wC
vP9‰w^AB%CKsE@,K@

P P P
v w
  J
L
 6 6 6
− =
vP9€w


P P P

v w
  J
L
 6 6 6
− =
vP9|w
K@KX*^‚@#E!m !K[#CWK!   KYEfƒ&\#lEItX!Z fq
^K[\#lEIt]6fqC%"#lEIt KYEfƒ&fq^K[ Kt  @KgD.K\E!M'
 _¡K@@KX*^‚Em!.*^K[Em%!%M*#lE!,EEm%!^K[!n!QE@P
D@D%E.D›P\‰4¢P:
ŽP;
 &@#] 
#P;P€\K@@KX*@y3@,KE!m !K[#E.\C^‚Ik*^K[Em%!%M*P
D@D%E.@D›P\7;¢P:
ŽP;
&@#]!a ^^,%!K[*'fJ*E. &'@O
%M*K@@KX*%!XsEh&+@D›P\‰:9¢P:
ŽP;
&@#]
CWK!a E!m !K[#E.\D@D%E.^AB%gD#@!,E
II. Electron cùng sự phát triển của Vật lý:
J.*^oK%M*%1!Y%@AB Ek@#lEEQE's&X!6%!h&*%M*h&6E.{!
3!6EE.KL%M*X!*!Y%"K%!& C%M*CNE@O"K.K "3!+6!#lE
h&*^KL#@X!K%!&'LI* ErE!s KWKC–#ZI* E!s KWKCK#Z#^tK
EAB @ &'EkC!,E!_CZ%H !n]“E!{%6%h&'@&NECNE@O3!+KE!*'




 GVHD:TSKH. Lê Văn Hoa

̀
ng
P4
^xK\"K^0 !1@3!+K%"!a h&'@&NE#WK^L63f‡ %!!a ^tK
EAB #WK
.AW%#P;::\z@–!CJ%!K[E^l
!Y%\E. CNE@O%x^KL%"#lECQ^-!n\
fAo !AX!Z h&*E.Y !A X!Z E!L
]nh&*^AB%!a Em!E6%M*!*K!X!*
!Y%!\!&_EAW%*'@DK !C K•D*#I
•D*I\%!XsEh&+@#lE^tKEAB !*'#lECNE
E!L" \%!˜ !,#lE ZKI*\%ƒ3!+K3!6E
g, @AB CWKEt%^lCZ!,!D!a
^)!@&NE# AoKE*EK@^0 zE!oK K*^"
E!{#lECNEE!L" %ƒ3!+K3!6E.*%6%I"
^K[Erv!AI" CZE&'s\6!I6 E!Q'^AB%\
!y%EK*•¡w!A!*&z#YKEƒItmf‡\#lE
CNEE!L" %ƒ3!+K3!6Eg,#lE @AB !A!*&E. %6%I" %"Eƒ
Itp# Ka*#lEC!*KE.K[&E.K[&I" #lE K_'%` !AE. %6%I" %"Eƒ
Itp# Ka*!*KC]*E.K[&E.K[&I" #lE K_'C{ItI" E. #lE K_'@
X!Z %" KWK!,\^K-&'%" !–*@Ex  @AB 3!6E.*@CZ!,
LE.6!%6KXsEh&+.£. @CZ@O'\!X!*!Y% AoK$%\*g@*%X
vP|7|ŽP;F€w\C#P;::^‚%!.p 6!I6 \EK*•C%6%I" X!6%X!Z
E!L^AB%3!6Eg,CWK#lEEt%^lEH'O#E!!Er 3!ƒ!QE^)!#Z  YK
@@AB Ek1a*\#…K#lE@AB Ek%" @AB !QE^)!\ @AB 
'% @Ws&EƒIt%M*I" % %*\C{CN'zEƒIt^M%*IJ3!6Eg,%!u
#lE@AB EkE!ZK%` %"E!L^ˆK!nK#lE @AB @W!1 @AB Ct
%"%M*CNE!ACN'IJ3!6Eg,zEƒIt%*3!+K^AB%.0E]WE^K\X!K^"Et%^l
#QE @AB %M*CNE#WK@!a&!,_'%!m!@-E+ ^ƒ&EK%!%1
!Y%@AB EkC*g@*%X^AB%%K@%!*^•%M*@OE!&'sE@AB Ek





 GVHD:TSKH. Lê Văn Hoa
̀
ng
'()*
PF
‚K^s#P;:7\X!K !K%$&!K[&$ h&* ^K[\]D.EGKIEDK
vP|€;ŽP;77w^‚Ikf‡  K+E!&'sE@AB Ek%M*@*%X^L K+KE!m%!%6%XsEh&+
E!J% !K[#g& h&*!!K[&$ h&* ^K[5p h&*K[#.p \]$%g,
^K[Er%"]+%!QE@AB Ekz#YK1K%!$X!Z %!u]" YE. %6%h&6
E.{!!Q3E!‡!*'3!6Eg,\ !–*@^_&^_&%` E•E,K@AB Ek6!I6 ¤G\
GKIEDK^‚ K+KE!m%!^AB%XsEh&+E!J% !K[#!sEI$%X!6%E!Ao !D K+
E!&'sE%M*Z \ @AB %M*]$%g,^K[Er%!u@&ZE•E,KfAWKf, @AB 
Ek!"*C]$%g,^K[Er@fˆ %6%@AB Ek6!I6  YK@%6%3!E
*&X!KE!&'sE3!E%M*GKIEDK.*^oKC
NE@O!Y%E!r*!N@A¥ Em!I" !,E%M*%M*6!
I6 \#P;9F\&KIfD5. @KDvP|;9ŽP;|€w\#lE
!CNE@OC@E!!CK%M* K*^{!h&mEl%!63
xKEKs \^‚E.E.zE.AW%IJE!NE@6!I6 %"
@A¥ Em!I" Ž!,E\E. X!K^"%6%%!QE@,K%!u%"
Em!!,EK-&'^tK#yECWKIJE!NE@6!I6 C
%6% %!QE ^-&@%6%f, %M* @AB \ %" E!L
%!&'L!"*%!!*&C%H E&_E!D%6%^tKg$
X!Z RE!oK K*%M*@OE!&'sEEA1 ^tK•KZ
+'.*O !–.p CNE%!QE%` %"@A¥ Em!^"\.p %6%!,E\!AD@D%E.
%!˜ !,\%` %"E!L%"Em!I" !&'L^l EJf%M*#lE!,E\!A
D@D%E.CWK @AB LCg& @AB 3%` %"E!LgD#!AIJE.&'-%M*

#lEI" 3!˜ ^1I•%CWKEƒIt "%¦CCD%E1I" XCWK#tK@K![ Ka*
%6%^,K@AB ^"]zK!a ![E!$% Kt !A![E!$% Ka*%6%^,K@AB ^"
E.  E.Ao !B33!E "K #lE %6%!Ex h&6E !1\ %!&'L ^l %M*
D@D%E.%` !A%M*EQE%+%6%!,ECK#Z^-&@h&6E.{!E.&'-I" R#lE
@,KI" #WKE.AW%^_'%!A*!-^AB%]KsE^s\ YK@I" D5. @KD
 D5. @KD^‚X!6Kh&6E!"*@A¥ Em!}I" R!,E~%M*6!I6 %!
%6%!,ECK#Z!AD@D%E.\3!E\1E.CC¡’ %!.p X!K#lE!,E
%!&'L^l EJf%" @AB Cg& @AB g6%^)!IŒEA1 $ CWK#lE




 GVHD:TSKH. Lê Văn Hoa
̀
ng
&KID5. @KD
5. @KD
+%,-
P7
I" 3!˜ ^1I•%@*E.&'-E!D3!A1 %!&'L^l %M*!,E\^AB%#ZE+
]zK!#I" 



L
 > 
H
ψ
 
− −

 ÷
 
=
r r
h

•@K-CWK]AW%I" CEƒItg6%^)!



λ
=
CWK3›#C

L

ν
=
" D5. @KD@@,KI" X!Z %" &• t%f*^l %1!Y%\%`
X!Z %" &• t%^K[Er\"@@,KI"  •@K-CWK!,ECNE%!QEX!K%!&'L
^l !6%CWKI" 6!I6 z%!…\ Ka*EƒItC]AW%I" X!Z %"h&*
![

ν
λ
=
5AW%I" D5. @KD@K![E.J%EKs3CWKX!tK@AB CCNEt%
%!&'L^l %M*!,E



 3
λ
=
LEK^6C)E.mCCNEt%E. EA1 @*K%M*#lE!,E\ AoKE*%ƒ
3!+K^C)E.mCCNEt%!K[E!oK%M*"#lE%6%!
%!m!g6%!A !CNE@O@AB EkE!KEK AoK
$%\‘D.D.DKID]D. vP;:PŽP;€‰wC##WK
%!u  9‰ E&xK\  Z ^‚ E.{! ]'   &' @O ]QE^)!
DKID]D. ^ƒ'Em!%6%!#, CE{#.*#lE![E!$% KWK!, Ka*^l%!m!




 GVHD:TSKH. Lê Văn Hoa
̀
ng
‘D.D.DKID]D. 
v@&
2
%9‰E&Z
b
Kw
P‰
g6%¤gC-EY*^lC^l%!m!g6%¤3C-g& @AB [E!$%%"Em!%6%!#,
CE!,E^ƒ&%"C•E^,'^AB%3!6E]KL&!sEI$%^1 K+!AI*&
¤g¤3§¨89
$%@s&E*E!KsEXs#lEE!m !K[#^Lg6%^)!C)
E.m%M*!,Ev%!˜ !,!AD@D%E.w#lE%6%!%!m!
g6%!QE%"E!L^AB%v]p %6%!@#%!¤g!n
!1w\E*IŒE!Q'.p X!K^"E*IŒX!Z E!L^^AB%

E!NEEtEg& @AB %M*"v¤3E.z.QE@Wwˆ
s&E*Ik*E!m !K[#^LE ^l%!m!g6%%M*3!“3^g& @AB E!{^l%!m!
g6%%M*3!“3^C)E.mIŒ}E•K~^K*IŒX!Z @#^AB% {E. %!&'['
m%!%M*!*K^l]QE^)!X!Z ]* Ko!n!1#lE@AB g6%^)!¤g!n
!1EQE's&fqEWK#lE¤3@W!1C AB%@,KKa*¤gC¤3E•E,K#lE#tK
h&*![]HE.r!ACN'![E!$%]QE^)!DKID]D.  KWK!,#lE%6%!%1]+
!KL&]KsE%!0 E*C-h&š^,%M*%6%^tKEAB @AB Ek




 GVHD:TSKH. Lê Văn Hoa
̀
ng
‘D.D.DKID]D.